arXiv subjects

Shuangge Ma

Publications and source records attributed to Shuangge Ma.

57 records · Page 4Linked to original sources

arXiv2008

Asymptotic properties of bridge estimators in sparse high-dimensional regression models

We study the asymptotic properties of bridge estimators in sparse, high-dimensional, linear regression models when the number of covariates may increase to infinity with the sample size. We are particularly interested in the use of bridge estimators to distinguish between covariates whose coefficients are zero and covariates whose coefficients are nonzero. We show that under appropriate conditions, bridge estimators correctly select covariates with nonzero coefficients with probability converging to one and that the estimators of nonzero coefficients have the same asymptotic distribution that they would have if the zero coefficients were known in advance. Thus, bridge estimators have an oracle property in the sense of Fan and Li [J. Amer. Statist. Assoc. 96 (2001) 1348--1360] and Fan and Peng [Ann. Statist. 32 (2004) 928--961]. In general, the oracle property holds only if the number of covariates is smaller than the sample size. However, under a partial orthogonality condition in which the covariates of the zero coefficients are uncorrelated or weakly correlated with the covariates of nonzero coefficients, we show that marginal bridge estimators can correctly distinguish between covariates with nonzero and zero coefficients with probability converging to one even when the number of covariates is greater than the sample size.

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arXiv2006

Penalized log-likelihood estimation for partly linear transformation models with current status data

We consider partly linear transformation models applied to current status data. The unknown quantities are the transformation function, a linear regression parameter and a nonparametric regression effect. It is shown that the penalized MLE for the regression parameter is asymptotically normal and efficient and converges at the parametric rate, although the penalized MLE for the transformation function and nonparametric regression effect are only $n^{1/3}$ consistent. Inference for the regression parameter based on a block jackknife is investigated. We also study computational issues and demonstrate the proposed methodology with a simulation study. The transformation models and partly linear regression terms, coupled with new estimation and inference techniques, provide flexible alternatives to the Cox model for current status data analysis.

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arXiv2005

Marginal asymptotics for the "large p, small n" paradigm: with applications to microarray data

The "large p, small n" paradigm arises in microarray studies, where expression levels of thousands of genes are monitored for a small number of subjects. There has been an increasing demand for study of asymptotics for the various statistical models and methodologies using genomic data. In this article, we focus on one-sample and two-sample microarray experiments, where the goal is to identify significantly differentially expressed genes. We establish uniform consistency of certain estimators of marginal distribution functions, sample means and sample medians under the large p small n assumption. We also establish uniform consistency of marginal p-values based on certain asymptotic approximations which permit inference based on false discovery rate techniques. The affects of the normalization process on these results is also investigated. Simulation studies and data analyses are used to assess finite sample performance.

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